how to insert shortcode into wordpress menu

You can't use shortcodes directly in the menu URL on the menu page, because the brackets get stripped out. But you can use placeholders like this: #profile_link#.

With the following code in functions.php, you can create a custom menu item with the URL #profile_link#, and it will replace that with your shortcode.

/**
 * Filters all menu item URLs for a #placeholder#.
 *
 * @param WP_Post[] $menu_items All of the nave menu items, sorted for display.
 *
 * @return WP_Post[] The menu items with any placeholders properly filled in.
 */
function my_dynamic_menu_items( $menu_items ) {

    // A list of placeholders to replace.
    // You can add more placeholders to the list as needed.
    $placeholders = array(
        '#profile_link#' => array(
            'shortcode' => 'my_shortcode',
            'atts' => array(), // Shortcode attributes.
            'content' => '', // Content for the shortcode.
        ),
    );

    foreach ( $menu_items as $menu_item ) {

        if ( isset( $placeholders[ $menu_item->url ] ) ) {

            global $shortcode_tags;

            $placeholder = $placeholders[ $menu_item->url ];

            if ( isset( $shortcode_tags[ $placeholder['shortcode'] ] ) ) {

                $menu_item->url = call_user_func( 
                    $shortcode_tags[ $placeholder['shortcode'] ]
                    , $placeholder['atts']
                    , $placeholder['content']
                    , $placeholder['shortcode']
                );
            }
        }
    }

    return $menu_items;
}
add_filter( 'wp_nav_menu_objects', 'my_dynamic_menu_items' );

You just need to set 'shortcode' in the $placeholders array, and optionally 'atts' and 'content'.

For example, if your shortcode is like this:

[example id="5" other="test"]Shortcode content[/example]

You would update:

'#placeholder#' => array(
    'shortcode' => 'example';
    'atts' => array( 'id' => '5', 'other' => 'test' );
    'content' => 'Shortcode content';
),

---

Note that I don't use do_shortcode() because it is a resource intensive function and isn't the right tool for the job in this case.

@Tim This code will work

put it in functions.php file

add_filter('wp_nav_menu_items', 'do_shortcode');